You have a multilingual site and you want the same post type to use different slugs in different languages?
You can do that if you are using a multilingual plugin, e.g. WPML.
(If you have a site that is a single language, e.g. Spanish, and you want the post type slugs to be Spanish—e.g. libro—then you would simply use that slug when you register the post type. You cannot use Types to change the slug of post types registered with other plugins.)
Yes, I have the WPML plugin installed. With it I have translated custom fields of the custom post without problems but I don't know when or how I can translate the slug of the custom post itself. Can you help me?
Check that and if you still have problems let us know, but in future if you have questions about translating I suggest you open a ticket in the WPML forum.